His theories on the Protestant ethic are controversial[1], but hardly "thoroughly debunked." As far as the Frankfurt School, uh, who cares? They drew from many political and social philosophies (including Marx who we often find at odds with Weber). It just seems completely uncharitable and tangential to bring it up.

[1] http://www.slate.com/blogs/the_world_/2013/08/29/is_the_prot...